NEW NGLAND COMMON ASSESSMENT PROGRAM...piece of paper and put in a bag. Mrs. Harrison will pick one piece of paper from the bag. On the ﬁ rst pick, it is more likely that the paper

NEW ENGLAND COMMON ASSESSMENT PROGRAM

Released ItemsSupport Materials

2006

Grade 4Mathematics

1NECAP_2006_Grade4_Math_Released V2

NECAP 2006 RELEASED ITEMSGRADE 4 MATHEMATICS

N&O 3.1 Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 999 through equivalency, composition, decomposition, or place value using models, explanations, or other representations; and positive fractional numbers (benchmark fractions: a/2, a/3, a/4, a/6, or a/8, where a is a whole number greater than 0 and less than or equal to the denominator) as a part to whole relationship in area and set models where the number of parts in the whole is equal to the denominator; and decimals (within a context of money) as a part of 100 using models, explanations, or other representations.

ID:202323 MI11-fruit.eps C Common

q Look at this set of fruit.

What fraction of the set of fruit is apples?

\ A. 38

\ B. 35

\ C. 58

\ D. 53



N&O 3.2 Demonstrates understanding of the relative magnitude of numbers from 0 to 999 by ordering whole numbers; by comparing whole numbers to benchmark whole numbers (100, 250, 500, or 750); or by comparing whole numbers to each other; and comparing or identifying equivalent positive fractional numbers (a/2, a/3, a/4 where a is a whole number greater than 0 and less than or equal to the denominator) using models, number lines, or explanations.

ID:202335 MI125-circles.eps C Common

w Look at these circles.

Which statement is true?

\ A. 23 is less than 2

4

\ B. 23 is equal to 2

4

\ C. 23 is greater than 2

4




ID:227055 MU51141_numberline.eps C Common

e Look at this number line.

0

F

114– 2

4– 3

4–

What fraction is equivalent to the fraction at point F on the number line?

\ A. 38

\ B. 23

\ C. 68

\ D. 64



N&O 3.3 Demonstrates conceptual understanding of mathematical operations by describing or illustrating the inverse relationship between addition and subtraction of whole numbers; and the relationship between repeated addition and multiplication using models, number lines, or explanations.

ID:227059 B Common

r Jan solved this problem.

346 + 251 597

Which number sentence could Jan use to prove her answer is correct?

\ A. 597 346+ =�\ B. 597 346− =�\ C. 346 251− =�\ D. 251 597+ =�



N&O 3.4 Accurately solves problems involving addition and subtraction with and without regrouping; the concept of multiplication; and addition or subtraction of decimals (in the context of money).

ID:227066 D Common

t The chart below shows how many tickets band members have sold to their concert.

Number of Tickets Sold

Adult 86

Child 51

The band members want to sell200 total tickets. How many more tickets do the band members needto sell?\ A. 137\ B. 127\ C. 73\ D. 63



G&M 3.1 Uses properties or attributes of angles (number of angles) or sides (number of sides or length of sides) or composition or decomposition of shapes to identify, describe, or distinguish among triangles, squares, rectangles, rhombi, trapezoids, hexagons, or circles.

ID:232578 AH144_triangle.eps D Common

y An artist is making a window. He needs a piece of glass in the shape of a triangle. All the sides of the triangle must be the same length. Which piece of glass can he use?

\ A.

\ B.

\ C.

\ D.



G&M 3.7 Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands.

ID:202397 AH152_needles.eps C Common

u Use a ruler to answer this question.

Which needle is exactly 6 centimeters long?

\ A.

\ B.

\ C.

\ D.



G&M 3.7 Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands.

ID:202387 MI172_Thinkbubble.eps A Common

i The height of a tree is 368 centimeters. Which measurement also shows the height of the tree?

100 centimeters = 1 meter

\ A. 3 meters 68 centimeters\ B. 36 meters 8 centimeters\ C. 36 meters 80 centimeters\ D. 300 meters 68 centimeters



F&A 3.1 Identifi es and extends to specifi c cases a variety of patterns (linear and non-numeric) represented in models, tables, or sequences by extending the pattern to the next one, two, or three elements, or fi nding missing elements.

ID:232502 B Common

o Look at this pattern.

50, 41, 32, ? , 14, 5

What number is missing in the pattern?\ A. 9\ B. 23\ C. 24\ D. 33



DSP 3.2 Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using most frequent (mode), least frequent, largest, or smallest.

ID:227106 TK0476_bike.eps C Common

a This line plot shows the number of miles each student in Mr. Miller’s class rode his or her bike last week.

1 2 3 4 5 6 7 8

Number of Miles0

× × × × × ×× × × × ×× × × ×

× × ××

Key

represents 1 student×

What was the greatest number of miles any student in the class rode his or her bike last week? \ A. 2\ B. 5\ C. 7\ D. 8



N&O 3.1 Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 999 through equivalency, composition, decomposition, or place value using models, explanations, or other representations; and positive fractional numbers (benchmark fractions: a/2, a/3, a/4, a/6, or a/8, where a is a whole number greater than 0 and less than or equal to the denominator) as a part to whole relationship in area and set models where the number of parts in the whole is equal to the denominator; and decimals (within a context of money) as a part of 100 using models, explanations, or other representations.

Scoring Guide

Score Description

1 Student has correct answer, 835.

0Response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured.

Blank No response

ID:227071 Common

s The chart below describes a number.

Hundreds Tens Ones

6 23 5

What is the number?



SCORE POINT 1(EXAMPLE B)

SCORE POINT 1(EXAMPLE A)

Student’s answer is correct.

ID:227071 Common


Hundreds Tens Ones

6 23 5

What is the number?

ID:227071 Common


Hundreds Tens Ones

6 23 5

What is the number?

Student’s answer is correct.





ID:227071 Common


Hundreds Tens Ones

6 23 5

What is the number?

ID:227071 Common


Hundreds Tens Ones

6 23 5

What is the number?

Student’s answer is incorrect.



Scoring Guide

Score Description

1 Student has a correct explanation.


Blank No response

Sample Response:

The shape cannot be a rhombus because the sides are all different lengths.


G&M 3.1 Uses properties or attributes of angles (number of angles) or sides (number of sides or length of sides) or composition or decomposition of shapes to identify, describe, or distinguish among triangles, squares, rectangles, rhombi, trapezoids, hexagons, or circles.

ID:227091 Common

d Dave read these clues about a shape.

• It has four sides.

• It has sides that are all different lengths.

Dave guessed the shape is a rhombus. Explain why Dave’s guess is correct or incorrect.




ID:227091 Common





Student’s explanation is correct.




ID:227091 Common





Student’s explanation is incorrect.



DSP 3.5 For a probability event in which the sample space may or may not contain equally likely outcomes, determines the likelihood of the occurrence of an event (using “more likely”, “less likely”, or “equally likely”).

Scoring Guide

Score Description

1Student completes table to show more girls than boys and a total of 20 students.


Blank No response

ID:224089 AH133_table.eps Common

f There are 20 students in Mrs. Harrison’s class. Each student’s name is written on a piece of paper and put in a bag. Mrs. Harrison will pick one piece of paper fromthe bag.

On the fi rst pick, it is more likely that the paper will have a girl’s name. On the chart below, write the number of girls and the number of boys that could be in Mrs. Harrison’s class.

Mrs. Harrison’s Class

Girls

Boys

Total 20

Students Number of Students



Sample Responses:

11 girls, 9 boys

12 girls, 8 boys

13 girls, 7 boys

14 girls, 6 boys

15 girls, 5 boys

16 girls, 4 boys

17 girls, 3 boys

18 girls, 2 boys

19 girls, 1 boy

20 girls, 0 boys








Girls

Boys

Total 20


Student has a correct answer.









Girls

Boys

Total 20










Girls

Boys

Total 20




SCORE POINT 0(EXAMPLE C)






Girls

Boys

Total 20





ID:232539 NECAP411-2_rectangles.eps Common

g a. Shade 12

of this rectangle.

b. Shade 24 of this rectangle.

c. Circle the statement that is true.

12

is greater than 24

12

is less than 24

12

is equal to 24



Blank No response

Sample Responses:

Part a:

Part b:

Part c: 12

is equal to 24

Scoring Guide

Score Description

2Student correctly shades both rectangles and makes a correct comparison in part c.

1

Student correctly shades both rectangles.

OR

Student makes a correct comparison in part c.





Student correctly shades both rectangles. (1 point)


g a. Shade 12

of this rectangle.



12

is greater than 24

12

is less than 24

12

is equal to 24

Student’s answer is correct. (1 point)






g a. Shade 12

of this rectangle.



12

is greater than 24

12

is less than 24

12

is equal to 24





Student’s answer is incorrect. (0 points)


g a. Shade 12

of this rectangle.



12

is greater than 24

12

is less than 24

12

is equal to 24







g a. Shade 12

of this rectangle.



12

is greater than 24

12

is less than 24

12

is equal to 24

Student does not correctly shade both rectangles.(0 points)






g a. Shade 12

of this rectangle.



12

is greater than 24

12

is less than 24

12

is equal to 24

Student does not correctly shade either rectangle.(0 points)



F&A 3.4 Demonstrates conceptual understanding of equality by showing equivalence between two expressions using models or different representations of the expressions; or by fi nding the value that will make an open sentence true (e.g., 2 + = 7). (limited to one operation and limited to use addition, subtraction, or multiplication)

Scoring Guide

Score Description

2Student writes the correct number, 1, and explains how he/she determined the answer.

1

Student writes the correct number.

OR

Student has a correct strategy with a minor computation error.


Blank No response

Sample Response:

Student explains that each side must equal 8.

ID:202494 Common

h Look at this number sentence.

2 4 8× = ×

What number makes the number sentence true? Show your work or explain how you know.




ID:202494 Common


2 4 8× = ×



ID:202494 Common


2 4 8× = ×


Student’s answer is correct and work is shown. (2 points)

Student’s answer is correct with no work or explanation.(1 point)




ID:202494 Common


2 4 8× = ×





DSP 3.1 Interprets a given representation (line plots, tally charts, tables, or bar graphs) to answer questions related to the data, to analyze the data to formulate conclusions, or to make predictions.

(IMPORTANT: Analyzes data consistent with concepts and skills in M(DSP)–3–2.)

ID:224101 NECAP309-reading_graph.ep Common

j This bar graph shows the number of minutes Danny read each day for a week.

Danny’s Reading Schedule

05

10

15

20

Mon

day

Tues

day

Wed

nesd

ay

Thurs

day

Min

ute

s D

anny

Rea

d

25

30

35

40

45

50

55

60

Frida

y

Satur

day

Sunda

y

a. How many more minutes did Danny read on Friday than he read on Thursday?

b. Use the bar graph to write a question for which the answer is 40 minutes.



Scoring Guide

Score Description

2Student gives the correct answer, 5 (minutes), for part a and writes a correct question or statement for part b.

1

Student gives the correct answer for part a.

OR

Student writes a correct question or statement for part b.


Blank No response

Sample Responses:

Part b: How many more minutes did Danny read on Sunday than Tuesday?

OR

How many minutes did Danny read on Monday and Wednesday combined?







05

10

15

20

Mon

day

Tues

day

Wed

nesd

ay

Thurs

day

Min

ute

s D

anny

Rea

d

25

30

35

40

45

50

55

60

Frida

y

Satur

day

Sunda

y



a) Student’s answer is correct. (1 point)

b) Student writes an appropriate question. (1 point)







05

10

15

20

Mon

day

Tues

day

Wed

nesd

ay

Thurs

day

Min

ute

s D

anny

Rea

d

25

30

35

40

45

50

55

60

Frida

y

Satur

day

Sunda

y




b) Student writes an appropriate question.(1 point)







05

10

15

20

Mon

day

Tues

day

Wed

nesd

ay

Thurs

day

Min

ute

s D

anny

Rea

d

25

30

35

40

45

50

55

60

Frida

y

Satur

day

Sunda

y




b) Student’s question cannot be answered with “40 minutes.” (0 points)







05

10

15

20

Mon

day

Tues

day

Wed

nesd

ay

Thurs

day

Min

ute

s D

anny

Rea

d

25

30

35

40

45

50

55

60

Frida

y

Satur

day

Sunda

y











05

10

15

20

Mon

day

Tues

day

Wed

nesd

ay

Thurs

day

Min

ute

s D

anny

Rea

d

25

30

35

40

45

50

55

60

Frida

y

Satur

day

Sunda

y



a) Student’s answer is incorrect. (0 points)








05

10

15

20

Mon

day

Tues

day

Wed

nesd

ay

Thurs

day

Min

ute

s D

anny

Rea

d

25

30

35

40

45

50

55

60

Frida

y

Satur

day

Sunda

y



a) Student’s answer is incorrect. (0 points)

b) Student’s answer is incorrect. (0 points)

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NEW NGLAND COMMON ASSESSMENT PROGRAM...piece of paper and put in a bag. Mrs. Harrison will pick one piece of paper from the bag. On the ﬁ rst pick, it is more likely that the paper